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Designs, Codes and Cryptography
Published in: Designs, Codes and Cryptography 5/2021

15-02-2021

Asymmetric entanglement-assisted quantum codes: bound and constructions

Authors: Hualu Liu, Peng Hu, Xiusheng Liu

Published in: Designs, Codes and Cryptography | Issue 5/2021

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Abstract

The theory of quantum error-correcting codes has been extended to asymmetric quantum channels-qubit-flip and phase-shift errors may have equal or different probabilities. Previous work in constructing quantum error-correcting codes has focused on code constructions for symmetric quantum channels. Recently, Galindo et al. introduced the concept of asymmetric entanglement-assisted quantum error-correcting (AEAQEC) code, and gave a Gilbert–Varshamov bound for AEAQEC codes. Then they present the explicit computation of the parameters of AEAQEC codes coming from BCH codes. In this paper, we first establish a bound for pure AEAQEC codes similar to the quantum Singleton bound, and introduce the definition of pure AEAQEC MDS codes. Then we construct three new families of AQEAEC codes by means of Vandermonde matrices, extended GRS codes and cyclic codes. The AEQAEC codes here have better parameters than the ones available in the literature.
previous article Constructions of doubly resolvable Steiner quadruple systems
next article Some constructions of quantum MDS codes
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Metadata
Title
Asymmetric entanglement-assisted quantum codes: bound and constructions
Authors
Hualu Liu
Peng Hu
Xiusheng Liu
Publication date
15-02-2021
Publisher
Springer US
Published in
Designs, Codes and Cryptography / Issue 5/2021
Print ISSN: 0925-1022
Electronic ISSN: 1573-7586
DOI
https://doi.org/10.1007/s10623-021-00845-z

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